SAN DIEGO, California (CNN) --Facing allegations that he groped women in incidents dating back over three decades, Republican Arnold Schwarzenegger apologized Thursday for behaving "badly," but also denounced the report as "trash politics."

Schwarzenegger, the leading candidate in California's gubernatorial recall race, addressed the allegations in the wake of a front-page story in the Los Angeles Times that detailed accusations from six women who charge that the actor-turned-politician inappropriately touched them.

In comments to supporters as he kicked off a four-day bus tour, Schwarzenegger said much of the story was "not true," but he then went on to apologize.

"Yes, I have behaved badly sometimes, yes it is true that I was on rowdy movie sets ... and I have done things I thought were playful that now I recognize that I have offended people," Schwarzenegger said.

He added, "I am deeply sorry about that and I apologize."

While Schwarzenegger said some of the accusations made against him were not true, but did not clarify which. His campaign issued a statement saying the story represented "a desperate attempt by Democrats so close to the election" to smear him.

The allegations came less than a week before the October 7 recall and as polls indicate growing support for Schwarzenegger.

Schwarzenegger launched his bus tour in San Diego, traveling north through the state over the next four days.

For his part, Davis was due to appear with Democratic presidential candidate Rep. Dick Gephardt of Missouri and Iowa Gov. Tom Vilsack, a continuation of his effort to portray the recall as part of a broader GOP campaign to challenge elections they lost.

Davis was re-elected to a second term in November, but his popularity has plummeted as the state deals with a budget crunch and lackluster economy.

"If we come together and unite against this recall, we will beat back this power grab and send a message form California to Crawford, Texas, to the White House: We are not going to stand for a Republican power grab," Davis said Wednesday at a rally with Democratic presidential candidate Wesley Clark.

Come Tuesday, California voters will decide whether to boot Davis out of office, and, on the second part of the ballot, they will pick from 135 names for a replacement should the recall succeed.

The question of whether to recall Davis will be decided by a majority of votes, but his successor -- if there is one -- only needs to pick up a plurality of votes.

Six women alleged that Schwarzenegger touched them in a sexual manner without their consent, according to the newspaper. The alleged acts date back to the 1970s, and the latest was in 2000. The newspaper contacted the women in the course of a seven-week investigation. None of the women approached the newspaper, the Times said.

Two of the six women in the Times report were identified; the other four requested anonymity, saying they feared retaliation. None of the women filed legal action against Schwarzenegger. None alleged that they were raped.

Three of the women said Schwarzenegger grabbed their breasts; another said he reached under her skirt and grabbed her buttocks. The fifth woman said he groped her and tried to remove her bathing suit in an elevator. The sixth charged that he pulled her on his lap and asked whether anyone had performed a certain sexual act on her.

One of the unidentified women told the newspaper that after Schwarzenegger touched her breast on a Santa Monica street in 1980, she made it clear that she didn't consider it playful.

She told the Times that she told him, "If I was a man, I would bust your jaw." Schwarzenegger, she said, just laughed.

Schwarzenegger has been dogged throughout the campaign by allegations that he mistreats women, prompting some women's groups to protest at his appearances. He has denied being a misogynist, and his wife, TV newswoman Maria Shriver, also has defended him against charges that he treats women badly.